Question

If $\alpha =3,\beta =5,\gamma =2,$ find the cubic polynomial

Answer 1

$\alpha =3,\beta 5,\gamma =2$

Cubic polynomial $\Rightarrow (x-\alpha )(x-\beta )(x-\gamma )$

$\Rightarrow (x-3)(x-5)(x-2)=0$

$\Rightarrow (x^2-8x+15)(x-2)=0$

$\Rightarrow x^3-8x^2+15x-2x^2+16x-30=0$

$\Rightarrow x^3-10x^2+31x-30=0$

$\therefore$ Cubic polynomial is $x^3-10x^2+31x-30=0$